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Bilinear mapping preserves quadratic Lyapunov functions between continuous-time and discrete-time LTI systems. This note studies if this property holds for other types of Lyapunov functions specified by vector norms of the system state. Some implications of the obtained results in the common Lyapunov function problems are discussed.
Several stability conditions derived for linear discrete-time interval systems by Myszkorowski (Automatica,30, 913-914, 1994) can be much more compactly rephrased with the aid of M-matrix theory.
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